Answer:
The 95% confidence interval for the mean is approximately;
(9.063, 9.737)
Step-by-step explanation:
The given parameters are;
The mean of the sample, [tex]\overline x[/tex] = 9.4
The sample variance, s² = 0.49
The sample size, n = 19
The confidence level = 95%
Therefore, we get;
[tex]CI=\bar{x}\pm t_{\alpha/2} \dfrac{s}{\sqrt{n}}[/tex]
The degrees of freedom, df = n - 1
∴ df = 19 - 1 = 18
From the t-table, the critical-t = 2.101
Therefore, we have;
[tex]CI=9.4\pm 2.101 \times \dfrac{\sqrt{0.49} }{\sqrt{19}}[/tex]
Therefore, we have;
9.4 - 2.101×√(0.49/19) < μ < 9.4 + 2.101×√(0.49/19)
9.0626 < μ < 9.737
∴ The 95% confidence interval for the mean ≈ (9.063, 9.737)
I Mark Brainliest ! No Bots Plz
Select All that apply
Answer:
Option 2
Step-by-step explanation:
1. A signal tower has two lights that are 30 feet apart from each other, one directly above the other. From
a boat, the angle of elevation of the lower light is 14 degrees, and the angle of elevation yo the upper
light is measured to be 32 degrees.
a) Find to the nearest foot the distance from the boat to the lower light.
b) The boat and the foot of the tower are in the same horizontal plane. Find to the nearest foot the
distance from the boat to the foot of the tower.
Solution :
It is given that the distance between the two lights is 30 feet.
The angle of elevation of the upper light from the boat, ∠ ABP = 32 degree
The angle of elevation of the lower light from the boat, ∠ ABQ = 14 degree
∴ ∠ PBQ = ∠ ABP - ∠ ABQ
= 32 - 14
= 18 degree
In triangle PAB
∠ PAB = 180 - (90 + 32)
= 58 degree
Similarly in triangle AQB
∠ AQB = 180 - (90 + 14)
= 76 degree
Now considering triangle PBQ and applying the sine theorem,
[tex]$\frac{PQ}{\sin 18}=\frac{BQ}{\sin 58}$[/tex]
we know PQ = 30 feet
∴ [tex]$BQ =\frac{\sin 58}{\sin 18} \times 30$[/tex]
= 82.33 feet
Again taking the right triangle ABQ and applying sine theorem,
[tex]$\frac{BQ}{\sin 90}=\frac{AB}{\sin 76}$[/tex]
[tex]$\frac{82.33}{\sin 90}=\frac{AB}{\sin 76}$[/tex]
∴ [tex]$AB = 82.33 \times \sin 76$[/tex]
= 79.88 ft
= 80 feet
HELPP!!!!!!!!!!!!!!!!
Answer:
D.4 3/4
Step-by-step explanation:
hope it helps you
which set of ordered pairs could be generated by an exponential function
Answer:
Option C represents an exponential function
Step-by-step explanation:
Generally, we have an exponential function in the form ;
y = a.b^x
Where in fact, a is not 0
In this case, let us have a as 1 and b as 2
So we have;
for x = -1
y = 2^-1 = 1/2
for x = 0
y = 2^0 = 1
for x = 1
y = 2^1 = 2
for x = 2
y = 2^2 = 4
So the correct choice here is the third option
Answer the question above
Answer:
MJ
Step-by-step explanation:
shxjsowibxkaowwkql
f(x)=3x+5 and g(x)=x^2
find g(3x)
Answer:
g(3x) = 9x²
Step-by-step explanation:
To evaluate g(3x) substitute x = 3x into g(x) , that is
g(3x) = (3x)² = 9x²
Jimmy invests $2,936 in a retirement account with a fixed annual interest rate of 5% compounded continuously. What will the account balance be after 18 years?
A) $6,599.86
C) $6,534.19
B) $7,221.39
D) $6,869.20
Answer:
B) $7,221.39
Step-by-step explanation:
Given data
Principal=$2,936
Rate=5%
n=12
Time = 18 years
The expression for compound interest is
A=P(1+r/n)^nt
substitute
A= 2936(1+0.05/12)^12*18
A= 2936(1+0.00416)^12*18
A= 2936(1.00416)^12*18
A= 2936(1.00416)^216
A= 2936*2.45149
A=7197.57464
Hence the approximate amount is B) $7,221.39
Emma is a professional cyclist. For the past year she has been practicing to ride as far as she can in a minute. At the beginning of the year, her personal record was 5/6 of a kilometer in one minute. After six months, she improved her record by 1/15 of a kilometer. After a year, she further improved her record by 1/12 of a kilometer. What is her best record?
Step-by-step explanation:
5/6+1/15+1/12in on minute
Emma's best record is 59/60 kilometers per minute.
Given that, Emma personal record was 5/6 of a kilometer in one minute.
What is addition of two fractions?To add fractions there are three simple steps:
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
Given, after six months, she improved her record by 1/15 of a kilometer. After a year, she further improved her record by 1/12 of a kilometer.
Now, 5/6 + 1/15 + 1/12
LCM of denominators 6, 15 and 12 is 60.
50/60 + 4/60 + 5/60
= 59/60
Therefore, Emma's best record is 59/60 kilometers per minute.
To learn more about the addition of fractions visit:
https://brainly.com/question/17544795.
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Solve the system by substitution.
x = 9y
x-5y=20
Step-by-step explanation:
hope this helps you! have a great day
The solutions of the system of equations are x = 45 and y = 5.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
The system of equations,
x = 9y .... (1)
x-5y=20 ......(2)
Substituting the value of x from the equation 1 to equation 2,
we get,
9y - 5y = 20
4y = 20
y = 5
Then, x = 5(9) = 45
Therefore, the solutions of the equations are x = 45 and y = 5
To learn more about the system of equation;
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The sum of the age of mother and daughter is 66 years.Mothers age is 5 times of daughters age.What is the age of daughter??
Answer:
I think it might be 13 or 14 I'm not completely sure though.
Step-by-step explanation:
Four cubes are lined up to form a solid. The side lengths of the cubes are 2 ft, 3 ft 4 ft. and 5 ft. What is the volume of the solar A. 196 ft B 224 ft C.374 ft3 d 2,744ft3
Answer:
A
Step-by-step explanation:
Oliver has created a plot of his backyard on the given coordinate plane, so that each unit length is one yard. He wants to design a right triangular plant bed for his backyard that has an area of eight square yards. After placing one vertex of the base of the plant bed at (3, 8) and one vertex at (7, 8) on his coordinate plane, he has to determine where to place the last vertex. Locate the possible locations of the last vertex on the coordinate plane.
Answer:
The possible locations are;
(3, 4), (3, 12), (7, 4), and (7, 12)
Please find attached the plot of the points created with Microsoft Excel
Step-by-step explanation:
The given parameters of the plot of Oliver's backyard are;
The area of the right triangular plant bed Oliver wants to design, A = 8 yd²
The length of a/each unit of the plot = 1 yard
The location of one of the vertex of the right triangular area = (3, 8)
The location of the other vertex of the right triangular area = (7, 8)
We note that the area of a triangle, A = 1/2 × Base length, B × Height, h
Let the distance between the two plotted point represent the base length, 'B', therefore;
B = 7 - 3 = 4 (We subtract only the x-values (7 and 3) given that the y-values (8 and 8) are the same;
Therefore, the base length, B = 4 yards
A = 1/2 × B × h
∴ A = 8 yd.² = 1/2 × 4 yd. × h
h = 8 yd.²/ 2 yd. = 4 yd.
The height of the right triangle, h = 4 yd.
Therefore the possible locations of the last vertex the right triangle on the coordinate plane, given that the first two points are parallel with the x-axis, are points 4 units above or the y-axis value of the plotted points with the x-value of the last vertex being either 3, or 7 as follows;
(3, 8 ± 4) or (7, 8 ± 4) which give points, (3, 4), (3, 12), (7, 4), and (7, 12).
Answer:
3,4 7,4
Step-by-step explanation:
Solve the question in the picture below. Thank you.
Answer:
8 units
Step-by-step explanation:
Find the distance along the y-axis. For the example points (3,2) and (7,8), in which (3,2) is Point 1 and (7,8) is Point 2: (y2 - y1) = 8 - 2 = 6. This means that there are six units of distance on the y-axis between these two points. Find the distance along the x-axis. Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.
is the Square root of 18 divided by 3 a rational or irrational number? explain using full sentences
Answer:
irrational
Step-by-step explanation:
[tex]\sqrt{18}[/tex] = [tex]\sqrt{9}[/tex] · [tex]\sqrt{2}[/tex] which is the same as 3[tex]\sqrt{2}[/tex]
3[tex]\sqrt{2}[/tex] divided by 3 equals [tex]\sqrt{2}[/tex], which is irrational
What is the positive solution to this equation?
4x2 + 12x = 135
Answer:
9/2
Step-by-step explanation:
I want its solution and the unit is about algebraic fraction.
Answer:
3x²/(3x - 9y)
This should be the simplest form.
Step-by-step explanation:
Combine the fractions:
(5x² - 2x²)/((6x - 6y) - (3y - 3x))
Combine like terms:
3x²/(6x - 3x - 6y - 3y)
Solve.
3x²/(3x - 9y)
Answer:
9x^2
======
6(x - y)
Step-by-step explanation:
Begin by switching the - to a plus. Switch the x and y in the second denominator.
5x^2 2x^2
===== + ======
6x - 6y 3x - 3y
Pull out the common factors in both denominators. Use the distributive property.
5x^2 2x^2
===== + ======
6(x - y) 3(x - y)
Multiply both the numerator and denominator by 2 on the left had fraction.
5x^2 2*2x^2
===== + ======
6(x - y) 2*3(x - y)
5x^2 4x^2
===== + ======
6(x - y) 6(x - y)
Put both numerators over a common denominator. Notice that the + sign shifts up. It shifts up because both fractions have been changed to a common denominator.
5x^2 + 4x^2
===================
6(x - y)
Combine the two numerators since they are of the same power.
9x^2
======
6(x - y)
The graph of a linear function is shown.
Which word describes the slope of the line?
• positive
• negative
O zero
O undefined
The slope of the line as shown in the graph of the linear function in the image below is: negative.
What is the Slope of a Line of a Linear Function?The slope of a line of a linear function = change in y/change in x.
The value of the slope would be positive if the graph increases upwards from your left to your right.
The value of the slope would be negative if the graph decreases downwards from your left to your right.
Thus, the slope of horizontal lines are always zero while the slope of vertical lines are undefined.
Therefore, the slope of the line as shown in the graph of the linear function in the image below is: negative.
Learn more about slope of linear functions on:
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help I literally got a 4/10 in my math test and my mom is like REALLLLY mad that she took my phone so I’m using my sisters ipad and she gave me advice on this app so i don’t even know if this could help but this is the page I need to complete/it’s for term 2 (week2) basically on my test well it’s apart of it so pls help- ~btw don’t look at the top cause I already completed it, I just need the 2 and 3 helppppp ima die ANDDD I used all the points I think that’s what it’s called~
Answer:
3/8 < 2/4
2/3 > 7/12
i could be wrong sorry
It should look like this:
2. The picture shows a feeding trough that is shaped like a right prism.
(a) Surface A and B are identical trapezoids. What are the lengths of the bases of the trapezoids? What is the height?
(b) Surfaces A and B will be painted blue. What is the total area that will be painted blue?
(c) The edges of the trapezoids need to be sanded. A piece of sandpaper advertises that it can sand up to 80 cm. Will one piece of sandpaper be enough to sand the edges of one trapezoid? Explain.
Answer:
B
Step-by-step explanation:
Find the slope and y-intercept for the graph.
God bless!
Find the product of (2a+b)^2
Answer:
(2a+b)^2
4a^2 + 4ab + b^2
product=4
Answer:
4a²+b²+4abStep-by-step explanation:(2a+b)²=(2a)²+(b)²+2×2a×b(a+b)²=a²+b²+2abanswer:- 4a²+b²+4abwhat is the angle M?
Answer:
The m in front of the angle notation refers to the measure of the angle labeled A, B and C (with vertex at B). By definition, the term congruent means "having equal length or measure". Figures are congruent ( ). Segments are congruent. Angles are congruent.Answer:
ive found sideNM = 9.797...
and constructed a triangle
Step-by-step explanation:
and I've measured it
the answer ive got is approximately 30 degrees
Lol I've verified in a funny way,
Ive measured the angle directly putting on the screen and it measures 30 degrees
A baseball team wins one out of every three games. How many wins
would they have after 27 games?
Answer:
9 wins
Step-by-step explanation:
[tex]\frac{1}{3} =\frac{x}{27} \\\\3x=27\\x=9[/tex]
They'd have 9 wins after 27 games.
You randomly pull a pen from a bag of pens. The bag has 1 red pen, 2
pink pens, 2 green pens, and 1 yellow pen.
What is the probability of drawing a red or a pink pen?
Answer:
For red you have a 1/5% chance for pink you have a 2/4% chance also know as 50% chance
Step-by-step explanation:
You have 3 dogs and they are playful. You decide that dogs are playful.
What type of reasoning is this?
•inductive
•deductive
Answer:
inductive
Step-by-step explanation:
1. Alex bought 2 buckets of baseballs that cost $19.49 each, a bat that cost $125.50, and 2 pair of baseball socks that totaled $29.50. The tax on Alex's purchases equaled $16. How much change did Alex receive if he paid with three $100 bills?
Answer:
$90.02
Step-by-step explanation:
Solve
Formula: Change money = paid money – bill. Paid money = change + bill.
Given: 2 buckets of baseballs that cost $19.49 each
A bat that cost $125.50, and 2 pairs of baseball socks that totaled $29.50
Tax on Alex's purchases equaled $16.
Paid with three $100 bills.
To find: How much change Alex received if he paid with three $100 bills
Total payment + Total Tax -Total cost
19.49 + 125.50 + 29.50 = 174.49 (Don't add the $16 tax because that will be taken from the amount we pay)
∴, three 100 bills is 300
So, 300 - 174.49 = 109.51
109.51 - 16 = 90.51
90.51 - 0.49 = $90.02
What is the negative zero of the quadratic function f(x) = 4x2 – 81?
Using The exterior angle Theorem solve for the identified angle
Answer:
107
Step-by-step explanation:
180-(65+42) = SQR = 73
180-73 = 107
6) Your car cost $42,500 when you
purchased it in 2017. The value of the
car depreciates by 15% annually.
a) Write an exponential function to
represent this situation.
b) How much will your car be worth
in 20242 Round your answer to the
nearest dollar.
HELP ME
Answer:
Step-by-step explanation:
Using exponential function concepts, it is found that:
The model is: .
The car will be worth $13,625 in 7 years.
This is geometry. Please help. If at all possible show solving steps or step explanations.